We employ advanced physical and mathematical methods to understand the biophysics of complex cellular processes. A major emphasis has been on the biogenesis of coated vesicles involved in clathrin mediated endocytosis (CME) and other intracellular transport processes. CME is the principal pathway for the regulation of receptors, and internalization of certain nutrients and signaling molecules, at the plasma membrane of eukaryotic cells. The early stage of receptor mediated endocytosis involves the formation of transient structures known as clathrin coated pits (CCPs) which, depending on the detailed energetics of protein binding and associated membrane transformations, either mature into clathrin coated vesicles (CCVs) or regress and vanish from the cell surface. The former are referred to as productive CCPs and the latter as abortive CCPs. We have developed a simple physical model for CCP dynamics and have carried out Monte Carlo simulations to investigate the time development of CCP size and explain the origin of abortive pits and features of their lifetime distribution. By fitting the results of the simulations to experimental data, we have been able to estimate values of the free energy changes involved in formation of the clathrin-associated protein complexes that comprise the coat, and have shown how the binding of cargo might modify the coat parameters and thereby facilitate CCV formation. We also have derived analytical expressions for the lifetime distribution and the distribution of maximum sizes of abortive pits, which may be useful in extracting additional information about the mechanism of CCP assembly from experimental data. Moreover, we have obtained a mathematical expression for the stochastic fate of a nascent pit, i.e., whether it will disassemble or mature into clathrin coated vesicles. This generalized expression is being used to identify parameters which affect particular processes in which clathrin-mediated endocytosis plays a role. In particular, we are investigating nanoparticles that are employed as drug delivery vehicles, to establish criteria that might be used when optimizing their design. Also, we are using atomic force microscopy (AFM) and single molecule force spectroscopy (SMFS) to characterize intermolecular interactions and domain structures of clathrin triskelions.To assess triskelion structure and triskelion-triskelion interactions, we subject purified individual triskelions, bovine-brain CCVs, and reconstituted clathrin-AP180 coats to AFM-SMFS pulling experiments and apply newly-derived analytics to extract force-extension relations from very large data sets. For individual triskelions, SMFS reveals a series of unfolding events associated with individual heavy chain alpha-helix hairpins containing ca. 30 amino acid residues. Cooperative unraveling of several hairpin domains up to the size of the known repeating motif of ca. 145 amino acid residues is also seen. We find that the clathrin lattices of AP180-mediated coats are energetically easier to unravel than those of native CCVs. The spectroscopic fingerprinting characteristics for single triskelions, clathrin-AP180 coats and CCVs vary noticeably and reveal non-trivial dependence on the force loading rate. Studies of clathrin assemblies expose weaker, but coordinated, clathrin-clathrin interactions that are indicative of the inter-leg associations essential for clathrin mediated endocytosis. In a related study, we having been using quartz crystal microbalance-dissipation (QCM-D) instrumentation to investigate the mechanical properties of the triskelions, and find that the apparent shear moduli of these structures to be approximately one to two orders of magnitude smaller than the Youngs modulus of a triskelion leg. The values of these shear moduli vary strongly with buffer properties and, to a lesser degree, also depend on properties of the substrate upon which a triskelion rests. This investigation is a continuation of our earlier work to establish the various mechanical properties of clathrin structures, which are important elements in physical models such as those mentioned above. In a different project, relating to mechanical aspects of cell response, we are establishing a reliable method for assessing the coupling between substrate properties and fundamental cell processes such as angiogenesis, neurogenesis and cancer metastasis which are thought to be modulated by extracellular matrix stiffness. The availability of matrix substrates having well-defined stiffness profiles can be of great importance in biophysical studies of cell-substrate interaction. We thus have developed a method to fabricate bio-compatible hydrogels with a well defined and linear stiffness gradient. This method, involving the photopolymerization of films by progressively uncovering an acrylamide/bis-acrylamide solution initially covered with an opaque mask, can be easily implemented with common lab equipment. It produces linear stiffness gradients of at least 40 kPa/mm, extending from <1 kPa to 80 kPa (in units of shear modulus). Hydrogels with less steep gradients and narrower stiffness ranges can easily be produced. The hydrogels can be covalently functionalized with uniform coatings of proteins that promote cell adhesion. Cell spreading on these hydrogels linearly correlates with hydrogel stiffness, indicating that this technique effectively modifies the mechanical environment of living cells. An extension of this work will focus on understanding the effects of substrate rigidity on the collective movements of mechanically-interacting cells. Such work may have applications in studies of wound healing, cancer metastasis, and normal and aberrant development of embryonic tissues. Finally, we are developing a high-throughput polyacrylamide (PA)-based stiffness assay which can be used to study how matrix stiffnes affects cell fate, particularly as it might mediate drug resistance. The gels were coated with collagen in order to facilitate cell attachment and proliferation. Polyacrylamide is the material of choice because it spans stiffness values from 0.3 to 300 kPa. The high-throughput format was chosen in order to facilitate obtaining dose response curves and to provide for simultaneous testing of multiple parameters. The assay is an improvement upon other techniques in terms of preparation time, robustness, and cost. This PA-based assay currently is being used to test the effect of stiffness on cancer cell responsiveness to anti-cancer drugs. In particular, we are testing multiple cell lines for their susceptibility to microtubule-targeting agents. By assessing cell viability and proliferation, and determining the drugs IC50, we should be able to establish how stiffness affects cancer cell responsiveness to these and other drugs.